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Convert angles between degrees and radians instantly. Essential for trigonometry, calculus, and engineering applications.
radians = degrees × (π / 180)
Example: 180° = 180 × (π / 180) = π radians ≈ 3.14159 rad
| Degrees (°) | Radians (rad) | Exact Value |
|---|---|---|
| 0° | 0.000000 | 0 |
| 30° | 0.523599 | π/6 |
| 45° | 0.785398 | π/4 |
| 60° | 1.047198 | π/3 |
| 90° | 1.570796 | π/2 |
| 120° | 2.094395 | 2π/3 |
| 135° | 2.356194 | 3π/4 |
| 150° | 2.617994 | 5π/6 |
| 180° | 3.141593 | π |
| 270° | 4.712389 | 3π/2 |
| 360° | 6.283185 | 2π |
Degrees are the most common unit for measuring angles. A complete circle is divided into 360 degrees. This system dates back to ancient Babylonian mathematics and is widely used in navigation, construction, and everyday applications.
Radians are the standard unit of angular measurement in mathematics and science. One radian is the angle created when the arc length equals the radius of the circle. A complete circle contains 2π radians (approximately 6.28318 radians).
Radians are essential in calculus, trigonometry, and physics because they simplify mathematical formulas. For example, derivatives of trigonometric functions (sin, cos, tan) are much simpler when angles are in radians. They are also used in circular motion, wave analysis, and signal processing.
Multiply the degree value by π/180 (or approximately 0.0174533). For example, 90° = 90 × (π/180) = π/2 ≈ 1.5708 radians.
π (pi) represents the ratio of a circle's circumference to its diameter. Since 180° is half a circle, it equals π radians. This relationship makes π fundamental to converting between degrees and radians.
Use radians for calculus, higher mathematics, physics calculations, and programming. Use degrees for navigation, surveying, construction, and everyday angle measurements where intuition matters more than mathematical simplicity.
Common conversions: 30° = π/6 rad, 45° = π/4 rad, 60° = π/3 rad, 90° = π/2 rad, 180° = π rad, 360° = 2π rad. Memorizing these helps with quick mental calculations in trigonometry.